Overlapping fiber gratings

ABSTRACT

Described are optical fibers, e.g., for use in stress-sensing or shape-sensing applications, that use overlapping grating configurations with chirped gratings to facilitate strain delay registration. In accordance with various embodiments, a fiber core may, for instance, have two overlapping sets of chirped gratings that differ in the direction of the chirp between the first and second sets, or a set of chirped gratings overlapping with a single-frequency grating. Also described are strain sensing systems and associated computational methods employing optical fibers with overlapping gratings.

CLAIM OF PRIORITY

This application is a continuation of and claims the benefit of priorityunder 35 U.S.C. § 120 to U.S. patent application Ser. No. 17/877,526,filed on Jul. 29, 2022, which is a continuation of and claims thebenefit of priority under 35 U.S.C. § 120 to U.S. patent applicationSer. No. 15/734,936, filed on Dec. 3, 2022, which is a U.S. NationalStage Filing under 35 U.S.C. 371 from International Application No.PCT/US2019/035429, filed on Jun. 4, 2019, and published as WO2019/236604 A1 on Dec. 12, 2019, which claims the benefit of priority toU.S. Provisional Patent Application Ser. No. 62/680,217, filed on Jun.4, 2018, each of which is incorporated by reference herein in itsentirety.

TECHNICAL FIELD

This disclosure relates generally to gratings inscribed in optical fibercores, and more specifically to grating configurations for strain delayregistration.

BACKGROUND

Optical fibers can be used as distributed optical sensors in manyapplications, for instance, to measure a physical parameter associatedwith the optical fiber, such as pressure, temperature, and thetwo-dimensional or three-dimensional shape of the fiber. Fiber-opticshape sensing is useful, for example, in industrial, recreational,medical, robotic, and other procedures where collocating a portion of atool with a portion of a shape-sensing optical fiber facilitatesdetermination of the location of the tool. As a further example,collocating a medical tool with a portion of a shape-sensing opticalfiber can help facilitate more precise determination of the location ofthe tool in robotic and non-robotic medical procedures. As a specificmedical example, in robotic or other computer-assisted surgery,collocating a surgical tool with a portion of the shape-sensing opticalfiber facilitates precise determination of the location of the tooloutside or within the patient's body based on the three-dimensionalfiber shape. The fiber shape can be computed from the bend, twist, andaxial strain along the optical fiber, which, in turn, are determinedbased on continuous strain measurements along multiple cores of thefiber. For accurate shape determinations, it is not only important tomeasure the strain accurately, but also to know where along the lengthof the fiber each strain measurement applies.

When an optical fiber is used as a sensor, the fiber is interrogated bysending light down the fiber and measuring reflections received fromvarious locations along the fiber; the spectral characteristics of thereflected light can be processed to provide information about localfiber properties, such as local strain. Fiber interrogation can beaccomplished, for instance, by optical frequency-domain reflectometry(OFDR), which uses a tunable laser scanned across a specified frequencyrange to provide the optical input signal. OFDR enables precisemeasurement of time-of-flight of the optical signal along the fiber.Core elongations of the fiber between two measurements can causereflections from the same piece of optical fiber to appear at differenttime delays in the two measured signals, and dynamic changes in thefiber during a laser scan can even cause reflections from the same pieceof optical fiber to appear at different time delays within a singlemeasured signal. Accordingly, matching strain measurements to particularphysical points of the optical fiber rather than to particular delays,herein referred to as strain delay registration, constitutes achallenging problem.

A previous approach to strain delay registration exploited Rayleighscatter correlations. Rayleigh scattering off the random microscopicdensity variations intrinsic to an optical fiber has the property thatit is delta-correlated (that is, the correlation signal exhibits adistinct maximum) in both the time domain and the spectral domain. Thisproperty allows a measured spectrum (corresponding to a temporal sliceof a spectrogram computed from a measured time-domain reflectionsignal), via correlations against a set of reference spectra with knowncorrespondence between time delay and physical location along the fiber,to be uniquely mapped to a particular reference spectrum and aparticular frequency shift relative to the reference spectrum, and thusto a particular location along the fiber and a particular strain at thatlocation. However, one problem associated with this approach is thatrandom reflectors can entail locations along the fiber where thereflection signal is of very low amplitude. A second problem withRayleigh scatter signals is that, at any point within the correlationsignal that does not correspond to the correct reference spectrum andthe correct frequency shift between the measured Rayleigh scatterspectrum and the reference spectrum, there will be no correlationmaximum and no indication where or how far away the correlation maximumis. Accordingly, only a complete search of the time-delay andfrequency-shift space can locate the correlation maximum.

Accordingly, an improved approach is desired.

SUMMARY

Described herein are optical fibers—for instance, for use in measuringphysical parameters such as in stress-sensing, temperature-sensing, orshape-sensing applications—that use overlapping configurations of fiberBragg gratings (FBS), including chirped gratings, to facilitate straindelay registration while avoiding the drawbacks associated with Rayleighscattering. FBGs are formed by at least locally periodic variations inthe refractive index of the fiber core, and provide a strong reflectionsignal that allows for accurate strain measurements. Determining thelocation of the measured strain along the fiber, however, is generallydifficult with FBGs having a uniform grating period, as the referencesignal taken with such uniform gratings results in a constant frequencyof the reflected signal across a range of time delays corresponding tothe length of the grating. By contrast, in a chirped grating, theperiodicity of the grating, and thus the frequency of the reflectedsignal, varies as a function of time delay, or position along the fiber.As a result, chirped gratings facilitate spatially resolving strainalong the fiber.

While a chirped grating by itself renders strain-induced frequencyshifts between reference and measurement signals indistinguishable fromtime-delay shifts undergone by a particular physical piece of the fiber(e.g., as a result of elongation), the combination of two overlappingsets of gratings (that is, gratings occupying a common fiber section)that are not chirped in the same manner can resolve this ambiguity. Forexample, a pair of counter-chirped gratings—one with increasing gratingperiod in a given direction and the other one with decreasing gratingperiodic in the same direction—has reflection peaks, for a given timedelay corresponding to a particular location along the fiber, atgenerally two frequencies. Strain at that location along the fibercauses the frequency of both peaks to shift in the same direction, whilea time-delay shift for the location results in frequency shifts inopposite directions. As another example, a chirped grating may becombined with a single-frequency grating to provide two reflection peaksfor a given location along the fiber. In this case, strain, again,results in the same frequency shift for both peaks, whereas a time-delayshift affects only the frequency peak of the chirped grating.

In a correlation signal obtained, for an optical fiber with overlappinggratings, by correlating a measurement spectrum at a given time delaywith reference spectra across a range of time delays (or vice versa),the correlation maxima fall on different lines for the differentrespective gratings, with slopes of the lines differing between gratingswith different chirps. The intersection of these lines, corresponding toa common correlation maximum, appears at the correct, disambiguated timedelay and frequency shift. The common maximum can be determined byperforming an exhaustive search over a range of time delays of thereference spectra that spans the maximum expected time-delay shiftrelative to the measurement spectrum. Alternatively, in accordance withvarious embodiments, the search space can be reduced by estimating thelocation of the common maximum based on extrapolation from correlationmaxima across frequency at two or more discrete points in time delay. Inthis manner, the use of overlapping gratings not identical in chirp cansubstantially reduce the computational cost of finding the correlationmaximum, e.g., as compared with Rayleigh-scattering-based techniques.

Accordingly, in a first aspect, this disclosure pertains to an opticalfiber including a fiber core having overlapping first and second sets ofgratings inscribed therein, and a cladding surrounding the fiber core.The first set of gratings includes one or more chirped gratingsextending over a section of the fiber, and the second set of gratingsincludes one or more gratings extending over the section of the fiberthat are not chirped like the one or more chirped gratings of the firstset of gratings. The first set of gratings and the second set ofgratings may each include a plurality of gratings that extendconsecutively over the section of the fiber. The section may extendsubstantially along an entire length of the optical fiber. In someembodiment, the one or more gratings of the second set of gratings is asingle-frequency grating. In other embodiments, the one or more gratingsof the second set of gratings are chirped, in an opposite direction tothe one or more chirped gratings of the first set of gratings. The oneor more chirped gratings of the first set and the one or more chirpedgratings of the second set may have a common grating length, and the oneor more chirped gratings of the first set of gratings may be offsetrelative to the one or more gratings of the second set of gratings byhalf the common grating length. A chirp rate of the one or more chirpedgratings of the first set of gratings may be equal in magnitude to achirp rate of the one or more gratings of the second set of gratings.The optical fiber may additionally include a single-frequency grating,wherein the single-frequency grating and the one or more chirpedgratings of the first set of gratings are consecutive gratings. Theoptical fiber may be a multicore fiber, that is, may include at leastone additional fiber core.

For each additional fiber core, the additional fiber core may likewisehave inscribed therein two overlapping sets of gratings, wherein a firstone of the two overlapping sets of gratings includes one or more chirpedgratings extending over the section of the fiber, wherein a second oneof the two overlapping sets of gratings includes one or more gratingsextending over the section of the fiber, and wherein the one or moregratings of the second one of the two overlapping sets of gratings arenot chirped like the one or more chirped gratings of the first one ofthe two overlapping sets of gratings.

In another aspect, this disclosure describes a method for measuringstrain along an optical fiber that includes first and second sets ofgratings inscribed in a fiber core of the optical fiber, wherein thefirst set of gratings overlaps with the second set of gratings, andwherein the first set of gratings includes one or more chirped gratingsand the second set of gratings includes one or more gratings that arenot chirped like the one or more gratings of the first set of gratings.The method includes interrogating the optical fiber in a reference stateof the fiber (e.g., an unstrained state) to obtain firsttime-delay-dependent reflection spectra resulting from combinedreflections off the first and second sets of gratings, wherein each timedelay of the first time-delay-dependent reflection spectra correspondsto an associated position of a plurality of positions along the fiber.The method further includes interrogating the optical fiber in astrained state of the fiber to obtain second time-delay-dependentreflection spectra resulting from combined reflections off the first andsecond sets of gratings, and then correlating the firsttime-delay-dependent reflection spectra with the secondtime-delay-dependent reflection spectra to determine correlation maximaacross time delay and frequency, each correlation maximum correspondingto a pair of a spectrum of the first time-delay dependent reflectionspectra and a spectrum of the second time-delay-dependent reflectionspectra, and to a frequency shift between the first and secondtime-delay-dependent spectra of the pair. For each of the correlationmaxima, a strain at a position along the fiber associated with the firsttime-delay-dependent reflection spectrum of the pair is then computedfrom the frequency shift associated with the correlation maximum.

To correlate the first time-delay-dependent reflection spectra with thesecond time-delay-dependent reflection spectra, the method may involvecorrelating, for each of the plurality of positions along the fiber, anassociated one of the first time-delay-dependent reflection spectra witheach of a plurality of the second time-delay-dependent reflectionspectra to determine a correlation maximum across time delays of thesecond time-delay-dependent reflection spectra and across frequency forthat position along the fiber. Alternatively, the method may involvecorrelating, for each of the second time-delay-dependent reflectionspectra, that second time-delay-dependent spectrum with each of aplurality of first time-delay-dependent reflection spectra to determinea correlation maximum across time delays of the firsttime-delay-dependent spectra and across frequency. The time delaysassociated with the plurality of second time-delay-dependent reflectionspectra in the first case (or the plurality of first time-delaydependent reflection spectra in the second case) may cover, at aspecified resolution, a range of time delays up to an expected maximumtime-delay shift, the range of time delays surrounding the time delayassociated with the respective one of the first (or second)time-delay-dependent reflection spectra. Alternatively, the correlationmaxima across time delay and frequency may each be determined by asearch performed near an estimated location of the respectivecorrelation maximum, the estimated location being obtained byextrapolation from pairs of correlation maxima across frequency, eachpair determined for a respective one of the plurality of the secondtime-delay-dependent reflection spectra in the first case (or theplurality of first time-delay-dependent spectra in the second case) andincluding a correlation maximum across frequency that is associated withthe first set of gratings and a correlation maximum across frequencythat is associated with the second set of gratings.

A further aspect pertains to a non-transitory machine-readable mediumstoring instructions, for execution by one or more hardware processors,that cause the processor(s) to perform the computational operations ofthe above-described method. In some embodiments, the instructions causethe hardware processor(s) to perform operations to determine strainalong an optical fiber by efficiently processing time-delay-dependentreflection spectra measured with the optical fiber. The optical fiberincludes a fiber core having first and second sets of gratings inscribedtherein, wherein the first set of gratings overlaps with the second setof gratings, and wherein the first set of gratings includes one or morechirped gratings extending over a section of the fiber and the secondset of gratings includes one or more gratings extending over the sectionof the fiber, the one or more gratings of the second set of gratings notbeing chirped like the one or more chirped gratings of the first set ofgratings.

The operations include, for each measured time-delay-dependentreflection spectrum of the measured time-delay-dependent reflectionspectra, correlating the respective measured time-delay-dependentreflection spectrum with a plurality of the time-delay-dependentreference reflection spectra to determine, for each of at least two ofthe plurality of time-delay-dependent reference reflection spectra, apair of correlation maxima across frequency, the pair of correlationmaxima including a correlation maximum across frequency associated withthe first set of gratings and a correlation maximum across frequencyassociated with the second set of gratings. Further, the operationsinclude extrapolating from the pairs of correlation maxima acrossfrequency to determine an estimated location of a correlation maximumacross time delay and frequency associated with the measuredtime-delay-dependent reflection spectrum; and then determining thecorrelation maximum across time delay and frequency by a search overcorrelations of the measured time-delay-dependent reflection spectrumwith time-delay-dependent reference reflection spectra near theestimated location. The operations also include computing the strain ata position along the fiber associated with a time-delay-dependentreference reflection spectrum at that correlation maximum from afrequency shift associated with the correlation maximum.

In yet another aspect, a strain measurement system is described. Thesystem includes an optical fiber as described above (i.e., a fiber witha core having overlapping first and second sets of gratings inscribedtherein, wherein the first set of gratings includes one or more chirpedgratings and the second set of gratings includes one or more gratingsnot chirped like those of the first set), a swept-wavelengthinterferometer system coupled to the fiber core and configured tomeasure reflection signals resulting from combined reflections off thefirst and second sets of gratings, and a computational processing unit.The swept-wavelength interferometer system may include a tunable laser.The computational processing unit is configured to convert the measuredreflection signals to time-delay-dependent reflection spectra, correlatethe time-delay-dependent reflection spectra with time-delay-dependentreference reflection spectra to determine correlation maxima across timedelay and frequency (each correlation maximum corresponding to a pair ofa spectrum of the time-delay dependent reflection spectra and a spectrumof the time-delay-dependent reference reflection spectra, and to afrequency shift between the time-delay-dependent reflection spectrum andthe time-delay-dependent reference reflection spectrum of the pair), andcompute, for each of the correlation maxima, a strain at a positionalong the fiber associated with time-delay-dependent referencereflection spectrum corresponding to the correlation maximum from anassociated frequency shift.

The optical fiber may include one or more additional fiber cores, eachlikewise having two overlapping sets of gratings (as described above)inscribed therein. In some embodiments, the cores of the optical fiberinclude a central fiber core and at least three peripheral fiber coreshelically wound around the central fiber core. Using measurements withthese four cores, the computational processing unit may compute, foreach of a plurality of positions along the fiber, from the associatedfrequency shifts determined for the fiber cores, an axial strain, a bendstrain, and a twist strain. The first and second sets of gratings mayextend substantially along an entire length of the optical fiber, andthe computational processing unit may be further configured to compute athree-dimensional shape of the optical fiber from the axial strain, bendstrain, and twist strain computed for the position along the opticalfiber.

In some embodiments, the second set of gratings is a single-frequencygrating. In other embodiments, the grating(s) of the second set ofgratings are chirped in an opposite direction to the chirped grating(s)of the first set of gratings. In this case, the gratings of the firstand second sets may have a common grating length, and their chirp ratesmay be equal in magnitude. Further, the fiber core may also include asingle-frequency grating consecutive with the first and second sets ofgratings. The system may further include a catheter, and thesingle-frequency grating may be located near a tip of the catheter.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing will be more readily understood from the followingdescription of various example embodiments, in particular, when taken inconjunction with the accompanying drawings.

FIG. 1A is a schematic drawing of an example optical fiber with auniform fiber grating inscribed therein in accordance with variousembodiments.

FIG. 1B is a plot of the refractive-index profile of the fiber gratingof FIG. TA.

FIG. 2A is a plot of the refractive-index profile of a chirped fibergrating in accordance with various embodiments.

FIG. 2B is a plot of the refractive-index profile of a gratingcounter-chirped to that of FIG. 4A in accordance with variousembodiments.

FIG. 2C is a plot of the refractive-index profile resulting fromsuperposition of multiple refractive-index profiles in accordance withvarious embodiments.

FIG. 3A is a schematic perspective view of part of a system forinscribing overlapping sets of gratings with chirped gratings into anoptical fiber in accordance with various embodiments.

FIG. 3B is a diagram of a phase mask in accordance with variousembodiments.

FIG. 4 is a flow chart of a method for inscribing overlapping sets ofgratings with chirped gratings into an optical fiber in accordance withvarious embodiments.

FIG. 5 is a graph showing, for four overlapping gratings inscribed intoa fiber core, the grating wavelength as a function of position along thefiber, in accordance with various embodiments.

FIG. 6A shows an example reference Bragg reflection spectrogram for anoptical fiber including a series of equally chirped overlapping fibergratings.

FIG. 6B shows an example correlation signal resulting from correlating,with the reference reflection spectrogram of FIG. 6A, a Bragg reflectionspectrum acquired with the same optical fiber for a given time delay.

FIG. 7A shows an example reference Bragg reflection spectrogram for anoptical fiber including sets of overlapping counter-chirped fibergratings, in accordance with various embodiments.

FIG. 7B shows an example correlation signal resulting from correlating,with the reference reflection spectrogram of FIG. 7A, a Bragg reflectionspectrum acquired with the same optical fiber for a given time delay.

FIG. 8A shows an example reference Bragg reflection spectrogram for anoptical fiber including a set of chirped fiber gratings overlapping witha single-frequency grating, in accordance with various embodiments.

FIG. 8B shows an example correlation signal resulting from correlating,with the reference Bragg reflection spectrogram of FIG. 8A, a Braggreflection spectrum acquired with the same optical fiber for a giventime delay.

FIG. 9 is a graph showing the signal amplitude, as a function of timedelay, of a Bragg reflection signal obtained with an optical fiberincluding sets of overlapping counter-chirped fiber gratings inaccordance with various embodiments.

FIGS. 10A and 10B show example Bragg reflection spectrograms forrespective optical fibers including sets of overlapping counter-chirpedfiber gratings consecutive with a single-frequency grating, inaccordance with various embodiments.

FIG. 11 is a flow chart illustrating methods of measuring strain alongan optical fiber with overlapping gratings, in accordance with variousembodiments.

FIG. 12 is a block diagram of an example strain measurement system inaccordance with various embodiments.

FIG. 13 is a block diagram of an example computing system for computingstrain along an optical fiber with overlapping gratings based oncorrelations between measurement and reference signals, in accordancewith various embodiments.

DETAILED DESCRIPTION

The present disclosure relates generally to optical fibers with fibergratings and to associated fiber-optic sensing systems and methods. FIG.1A schematically illustrates an example single-core optical fiber 100with a single uniform fiber grating inscribed therein. As shown, theoptical fiber 100 includes a fiber core 102 surrounded by a cladding104. The fiber 100 may be made of silica, with a dopant, such asgermanium, added to the core 102 to increase the refractive index n₂ ofthe core 102 relative to the refractive index n₁ of the cladding 104,causing light to be guided in the core 102 by total internal reflectionat the interface between core 102 and cladding 104. Optionally, thecladding 104 may be surrounded by a fiber coating (not shown).

Germanium-doped fiber cores (among others) are photosensitive, allowingthe refractive index to be changed by exposure to ultraviolet (UV)light. This property can be used to create a grating 106 in the core 102by periodically varying the refractive index along the longitudinal axis108 of the fiber, e.g., between n₂ and a different refractive index n₃.The grating 106 may span a certain length l, as shown, or extend alongthe entire length of the fiber. The grating period Λ, that is, thedistance between two adjacent refractive-index maxima, determines thepeak wavelength λ_(B) and frequency f_(B) (called the “Bragg wavelength”and “Bragg frequency,” respectively) at which the grating 106 reflectslight: λ_(B)=2n_(e)Λ. and f_(B)=C/λ_(B), where n_(e) is the effectiverefractive index of the fiber core 102 and c is the speed of light. Inaccordance with various embodiments, gratings with Bragg wavelengths inthe vicinity of 1550 nm are used. FIG. 1A schematically depicts therefractive index in the grating 106 as varying between two discretevalues, in accordance with a square wave function. In practice, therefractive-index profile of a grating is usually more akin to asinusoidal, as shown by the example refractive index profile of FIG. 1B(plotted as a function of position along the fiber). A uniform fibergrating as illustrated in FIGS. 1A and 1B, that is, a grating with aconstant grating period, exhibits a narrow reflection peak at the Braggfrequency and at a particular time delay that depends on the location ofthe grating along the fiber.

With reference now to FIGS. 2A-2C, refractive index profiles of chirpedfiber gratings as used in accordance with various embodiments are shown.In a chirped grating, the grating period Λ varies as a function ofposition along the axis of the fiber. As a consequence of the change inthe grating period Λ, the Bragg wavelength λ_(B) and frequency f_(B)likewise change along the axis of the fiber, resulting in a broaderreflected spectrum and a time-dependent reflection signal that changesin frequency, e.g., as shown below in FIG. 6A. In FIG. 2A, the gratingperiod Λ decreases monotonically towards the right. FIG. 2B shows arefractive-index profile that is counter-chirped to that of FIG. 2A.That is, while the grating period in FIG. 2A decreases (and the Braggfrequency, accordingly, increases) towards the right, the grating periodin FIG. 2B increases (and the Bragg frequency, accordingly, decreases).In accordance with various embodiments, counter-chirped gratings arewritten into an optical fiber core in an overlapping manner. Toillustrate, FIG. 2C shows the refractive-index profile resulting fromsuperposition of multiple counter-chirped refractive-index profiles.

Various well-known techniques are available to inscribe fiber gratingsinto a fiber core. Uniform gratings can be created efficiently bytwo-beam interference, where a UV laser beam is split into two beamsthat interfere, at the location of the fiber, to create a periodicintensity distribution along the interference pattern. Since the amountof the refractive-index change depends on the intensity of the light (inaddition to the duration of exposure), this intensity distributionresults in a periodic refractive-index change corresponding to theinterference pattern. To create a non-uniform grating, a shortinterference pattern may be varied as the optical fiber is translatedalong the pattern, resulting, effectively, in a sequence of small,partially overlapping gratings. Alternatively, an appropriatediffraction grating (such as a fused silica transmission grating,typically called a phase mask) may be placed between the UV light sourceand the fiber. The phase mask conveniently creates a two-beaminterference pattern at the location of the fiber using the +1 and −1diffraction orders. Yet another option is to write the grating into thefiber core point-by-point, using a tightly focused laser beam, thepoints spaced at the desired grating period. This method allows writingdifferent gratings into different cores of a multicore fiber. Bycontrast, using two-beam interference or phase masks, the same type ofgrating is written simultaneously into all cores of the fiber.

FIG. 3A schematically illustrates, in perspective view, parts of anexample system 300 employing phase masks to efficiently inscribeoverlapping sets of gratings (including one or more sets of chirpedgratings) into an optical fiber in accordance with various embodiments.(Note that the drawing is not to scale.) As shown, the system includes aUV laser 302, a variable aperture 304 (e.g., driven by a micrometer), aphase mask holder 306 mounted on a translation stage (not shown), andfiber guides 510. The phase mask holder 306 may hold one or more phasemasks. For example, in the embodiment shown in FIG. 3B, the phase maskholder 306 holds three horizontally aligned phase masks 312, 313, 314arranged in a column. The phase masks 312, 313, 314 may be held inplace, for instance, by a clamping mechanism.

The phase mask holder 306 is placed in the UV beam 316 generated by thelaser 302, oriented with its normal parallel to the beam axis (hereinthe x-direction). Via the translation stage, the phase mask holder 306can be moved relative to the beam 316 in the y and z directions, e.g.,using respective micrometers, which may be motorized. Translation in thez direction allows selecting one of the three phase masks 312, 313, 314.The fiber guides 310, which are placed at fixed lateral positionsrelative to the phase mask holder 306, ensure a horizontal orientationof an optical fiber 318 at a fixed short distance in front of theselected phase mask (on the side opposite the laser 302), e.g., byrunning the fiber 318 through horizontal grooves in the fiber guides310. The fiber 318 is movable along its length (i.e., in the ydirection) in front of the phase mask 312, 313, 314, e.g., using aprecision transport mechanism (not shown), to enable gratings to bewritten into different fiber portions. The variable aperture 304, whichis placed between the laser 302 and the phase mask holder 306, at afixed position centered on the UV beam 316, allows adjusting the widthof beam 316 that is passed to illuminate the phase mask 312, 313, or 314and fiber 318.

Among the three phase masks 312, 313, 314 shown in FIG. 3B, the linespacing of one phase mask has a uniform period across the phase mask,and the line spacing of the other two phase masks is chirped, i.e., itsperiod increases or decreases from one side of the phase mask to theother side. The chirped phase masks 313, 314 are identical, but one isrotated by 180° relative to the other in the plane of the phase mask(or, put differently, is oriented upside-down) to reverse the directionof the chirp. The chirped phase masks 313, 314, and thus the gratingsthey create, may be linear in chirp, i.e., have a constant chirp rate,for example, of 2 nm/mm. With this chirp rate, a grating that is, forexample, 10 cm in length, covers a 200-nm wavelength range. To write agrating covering a specified wavelength range at a given chirp rate, thecorresponding grating length can be set by adjusting the beam width viathe aperture 304. The width of the aperture 304 may be set, for example,to 2.5 mm to write a grating that is 2.5 mm in length and spans a 5-nmwide wavelength range. The location of that 5-nm range along theavailable spectrum can be selected by laterally translating the phasemask 313 or 314 in the y direction, using the translation stage, toposition the beam 316 on the respective portion of the phase mask 313 or314.

FIG. 4 is a flow chart of an example method 400 for inscribingoverlapping sets of gratings (including chirped gratings) into one ormore cores of an optical fiber, in accordance with various embodiments.The method 400 may be implemented using, for instance, the system 300 ofFIGS. 3A and 3B. In general, the method 400 includes multiple passesthrough a given section of the fiber (e.g., in some embodiments, theentire length of the fiber), each pass creating one set of gratingsextending over the section. Different passes generally differ in thechirp rate and/or the covered Bragg wavelength range of the inscribedgratings. The grating length may (but need not necessarily) be the samefor all passes. The wavelength ranges associated with the differentpasses may be selected such that, together, the multiple sets ofgratings cover a certain wavelength range. For example, in someembodiments, a 30-nm wavelength range is achieved with six sets ofgratings, each covering a 5-nm wavelength range.

Assuming that the same grating length is used for all passes, the method400 begins by setting the aperture 304 to the requisite width to achievethe desired grating length (act 402). For each pass, a phase mask withthe desired chirp rate and direction is selected, e.g., among the phasemasks 312, 313, 314 (act 404), and moved into the UV beam 316 (e.g.,using the z stage of the translation stage 308), and the phase mask ispositioned relative to the aperture to select a desired wavelength rangealong the phase mask (act 406). The fiber is illuminated to write a setof gratings of the set length and wavelength range into the core (act408), and then the fiber is translated along its axis to put the fiberin place for the inscription of the next grating (act 410); in order towrite consecutive gratings, the fiber is moved by the grating length.The process is iterated to sequentially write a set of gratingsextending over the entire section of fiber, moving the fiber across thephase mask in increments of the grating length in between inscriptionsteps. After the pass has been completed, i.e., the end of the sectionshas been reached (act 412), the fiber is translated back to thebeginning of the section (act 414), possibly with an offset (e.g., asillustrated below with reference to FIG. 7A). The phase mask for thenext pass is then selected and, if it differs from the previously usedphase masked, moved into the UV beam 316 (act 404). If needed, the phasemask is laterally translated to select the next wavelength range (act406). The next set of gratings is then written into the fiber core(s) byalternatingly writing a grating and translating the fiber by the gratinglength (acts 408, 410). (Alternatively, the fiber may be movedcontinuously, and the laser may be pulsed based on measurements of thefiber position to write the gratings in the proper places. With pulselengths of, for instance, 10 ns, the fiber motion is practicallyfrozen.) Additional passes through the fiber take place as needed towrite the desired number of overlapping sets of gratings.

The method 400 can be varied in a number of ways. For example, when oneof the passes involves writing a uniform (rather than chirped) grating,it may be beneficial to adjust the grating length to a higher value(e.g., a multiple of the grating length of a chirped set of gratings) tofacilitate covering the section of the fiber in fewer iterations of acts408, 410. Grating-length adjustments may take place at the beginning ofeach pass, e.g., before or directly after the selection and positioningof the phase mask (in acts 404, 406). Further, in some embodiments, thephase mask may be switched out within a given pass, e.g., to write auniform grating in line with gratings having non-zero chirp (non-zerophase variation) (e.g., as illustrated in FIGS. 9 and 10 ). The samesequence of gratings can be achieved, alternatively, by skipping asubsection of the fiber when writing the chirped gratings, and writingthe uniform grating into the skipped subsection in a separate pass. Ingeneral, by translating the fiber by amounts other than the gratinglength, the method 400 allows for writing gratings non-consecutively,with gaps between neighboring gratings or, conversely, with overlapbetween gratings written in the same pass. In accordance with variousembodiments, however, consecutive gratings are beneficial to enablestrain determinations along the entire length of the section. It is alsonoted that the precise order of steps in method 400 as depicted in FIG.4 need not necessarily be followed in each embodiment. For example, witha precisely controlled translation stage 308 and aperture 304, theadjustment of the aperture width (act 402), the selection and verticalpositioning of the phase mask (act 404), and the horizontal positioningof the phase mask (act 406) can generally performed in any order.

FIG. 5 illustrates an example grating configuration 500 with fouroverlapping sets of chirped gratings in a graph of grating (or Bragg)wavelength as a function of position along the fiber. The gratingwavelength is shown along the vertical axis, and the position along a1-cm long section of the fiber is indicated along the horizontal axis.This graph is an ideal representation of the spectrograms that will bedescribed in a later section. Each individual grating corresponds to adiagonal line in the graph, reflecting a decrease or increase inwavelength along the fiber section. The four sets of gratings, eachcreated during a respective pass through the fiber section, are shown asfour respective “rows” of such diagonal lines. As can be seen, thegratings all share a common grating length of 2.5 mm and a chirp-ratemagnitude of 2 nm/mm such that each row of grating spans a 5-nmwavelength range. The wavelength ranges corresponding to the four setsof gratings are consecutive so that the four rows, collectively, span a20-nm range, from 1530 nm to 1550 nm. Along this wavelength range,down-chirped gratings (whose frequency decreases down the length of thefiber) alternate with up-chirped gratings (whose frequency increasesdown the fiber). Thus, within a pair of adjacent gratings, the gratingsare counter-chirped. Further, as shown, the up-chirped gratings areoffset relative to the down-chirped gratings by half the common gratinglength.

The grating configuration 500 of FIG. 5 is one example of configurationsuseful for accurately and precisely determining both strain and thelocation along the fiber where the strain occurs. In general, inaccordance with various embodiments, grating configurations thatfacilitate strain delay registration include two or more overlappingsets of gratings, at least one set of gratings being chirped, withdifferent sets of gratings differing in the direction of the chirpand/or in the magnitude of the chirp rate (allowing for uniform,non-chirped gratings, which have a chirp rate equal to zero). As will beexplained below, overlapping sets of gratings that are not chirped inthe same manner generally result in unique maxima across a range of timedelays and frequency shifts in a correlation signal, facilitating strainmeasurements to be uniquely associated with locations along the fiber.

In the following, Bragg reflection spectrograms and associatedcorrelation signals for various grating configurations will bedescribed. In accordance herewith, a measured time-domain reflectionsignal is generally processed by short-time Fourier transform (STFT).For each point in the time-domain data, STFT creates a reflectionspectrum (that is, computes a signal amplitude as a function offrequency) by Fourier-transforming a short segment of the time-domainsignal associated with (e.g., beginning at) that point. The resultingspectra are stacked along the time dimension to obtain a two-dimensionaltime-frequency image of the signal, commonly referred to as aspectrogram.

Let the two-dimensional function s(f, t) denote the reflection-signalamplitude (i.e., the amplitude of the spectrogram) as a function of timedelay and frequency, and let the one-dimensional function s(f|t) denotethe reflection spectrum, i.e., the reflection-signal amplitude as afunction of frequency, at a given time delay t. Further, let thesubscript “ref” denote a reference signal or spectrum. Thecross-correlation between a reflection spectrum s(f|t) at time delay tand a reference reflection spectrum s_(ref) (f|t′) at time delay t′ isthen given by:

c(Δf|t,t′)=∫s _(ref)(f|t′)s(f+Δf|t)df,

which is a function of the frequency shift Δf between the spectrums(f|t) and the reference spectrum s_(ref) (f|t′). In accordance withvarious embodiments, each (time-delay-dependent) reflection spectrums(f|t) of a measurement signal is cross-correlated (herein also simply“correlated”) with each of a plurality of reference reflection spectras_(ref) (f|t′) that collectively cover a range of time delays t′including the respective time delay t of the measurement spectrum. Thisrange may be, e.g., a symmetric range up to maximum expected time-delayshift Δt between measurement and reference signals, t−Δt≤t′≤t+Δt, or, iftime-delay shifts are expected in only one direction, an asymmetricrange, e.g., t−Δt≤t′≤t. The cross-correlations are assembled across therange of time delays t′ into a correlation signal as a function of timedelay t′ and frequency shift Δf, c(t′,Δf|t). If the spectrum measured attime t is time-delay-shifted by Δt and frequency-shifted by Δf withrespect to the reference spectrum originating from the same location ofthe fiber, the correlation signal will have a peak, or maximum, att′=t−Δt, Δf. Accordingly, by identifying a (unique) correlation peak inthe correlation signal c(t′,Δf|t) for each measurement spectrum s(f|t),the measurement signal can be mapped onto pairs of a time delay t′ ofthe reference signal (corresponding to a particular location on thefiber) and an associated frequency shift Δf (corresponding to strain atthat location), and, thus, to strain as a function of position along thefiber. In some embodiment, the correlation function, instead ofreflecting cross-correlations of a single measurement spectrum with arange of reference spectra, assembles the cross-correlations of a singlereference spectrum, corresponding to a particular location along thefiber, with measurement spectra covering a range of time delays.Aggregated over all reference spectra, the varied correlation signalsc(t, Δf|t′) result in the same determination of strain along the fiber.

It is noted that correlation signals may be (and are herein) shown as afunction of time delay and a frequency that corresponds to the sum ofthe frequency shift and some fixed-frequency offset. For example, whencorrelating measured reflection spectra with the spectra of asingle-frequency grating, the frequency shift may be offset by the Braggfrequency of the single-frequency grating, to associate each correlationpeak with the actual reflected Bragg frequency at the respective fiberlocation. From the frequency of a correlation peak, the associatedfrequency shift can, of course, be straightforwardly calculated. Herein,reference to correlating spectra, or determining correlation maxima,“across frequency” shall be understood as synonymous with correlatingspectra, or determining correlation maxima, “across frequency shift.”

With reference to FIGS. 6A and 6B, for comparison with overlapping,differently chirped sets of gratings in accordance herewith, considerfirst the Bragg reflection spectrogram and associated correlation signalfor an optical fiber including a set of equally chirped overlappingfiber gratings. In the spetrogram of FIG. 6A, the spectral peaks showthe frequency of such as set of chirped gratings as a function of timedelay, corresponding to the location along the fiber. As can be seen,the gratings partially overlap, each grating being translated by a thirdof the grating length relative to its immediate neighbor(s), resulting,in conjunction with the chirp, in three Bragg reflection peaks for eachtime delay.

FIG. 6B shows an example correlation signal resulting from correlating,with the spectrogram of FIG. 6A as a reference, a Bragg reflectionspectrum acquired with the same optical fiber for a particular timedelay. (Note that the correlation signals as depicted in FIGS. 6B, 7B,and 8B cover the entire range of the respective reference reflectionspectrograms shown in FIGS. 6A, 7A, and 8A. Also, the vertical axisreflects the frequency shift only up to some arbitrary offset.) Thecorrelation signal forms parallel diagonal lines, brightest in a centersection, shifted relative to each other in time delay by the time-delaydistance of two neighboring gratings in the reflection signal of FIG.6A. If this time-delay distance is greater than the maximum expectedtime delay between reference and measurement signals (which is generallylimited due to physical considerations, such as maximum expectedstrains), each measurement spectrum can be mapped onto one of the linesin the correlation signal. That does, however, not resolve the ambiguitybetween strain effects and time-delay effects presented by the line.Thus, although the chirped gratings provide a wideband reflection signalas generally affords good resolution, they do not allow for strain delayregistration.

Referring now to FIGS. 7A and 7B, a Bragg reflection spectrogram andexample associated correlation signal for an optical fiber including twooverlapping sets of counter-chirped fiber gratings in accordance withvarious embodiments are shown. As can be seen in FIG. 7A, the time-delaydependent Bragg frequencies for the two sets of gratings form a“herringbone” pattern, with a set of up-chirped gratings covering afirst range of frequencies and a set of down-chirped gratings covering asecond range of higher frequencies that is consecutive with the firstrange. Neighboring gratings within each set are translated by thegrating length, i.e., the gratings are consecutive (without overlap). Asbetween the two sets, the gratings are shifted. In the example shown inFIGS. 7A-7B, the shift is by half a grating length, and otherimplementations may use sets of gratings with other amounts of shift(such as by a third grating length, quarter grating length, a fifthgrating length, etc.). In some implementations, the two sets of gratingsmay have zero shift, although zeros can occur in the signal amplitude atlocations where the Bragg frequencies of the two overlapping gratingsare the same, which causes destructive interference of the reflectedlight in the event that the refractive-index maxima of one grating areshifted by half a grating period relative to those of the other grating.Therefore, it is beneficial to laterally offset the overlapping gratingsby some non-zero amount.

As shown in FIG. 7B, the correlation of a spectrum at a given time delaywith the spectra of FIG. 7A used as a reference forms two sets ofparallel lines, corresponding to the two sets of gratings. Each set oflines may include, for each individual grating, multiple (e.g., asdepicted, two) lines within the respective time-delay range. Thevertical separation between these lines (e.g., the vertical separationbetween the lines 700, 702 within time-delay range 704) generally variesas a function of the particular time delay, and corresponding locationwith the reflection pattern, where the measurement spectrum is obtained.Due to their different orientations (or gradients), some lines from oneset intersect with some lines from the other set (e.g., line 702intersects with lines 706, 708), forming distinct correlation peaks 710in time delay and frequency (corresponding to frequency shift) thatrepeat only at intervals corresponding to half the grating length,largely resolving the ambiguity between time-delay shifts and frequencyshifts.

Intuitively, the cross-correlation between a measurement reflectionspectrum and a reference reflection spectrum originating from the samelocation along the fiber will result in a single correlation peak acrossfrequency, the frequency shift associated with the peak (if any)resulting from fiber strain at that location. By contrast, as betweentwo reflection spectra (e.g., a measurement reflection spectrum and areference reflection spectrum) measured for two different locationsalong the fiber, one will generally exhibit reflection peaks atfrequencies that are farther apart or closer together than thereflection peaks of the other. To illustrate, in FIG. 7A, the reflectionpeaks 720, 722 at time delay 250 are closer together than the reflectionpeaks 724, 726 at time delay 200. As a result, the cross-correlationbetween a measurement reflection spectrum and a reference reflectionspectrum originating from two different locations along the fiber willgenerally result in two correlation peaks across frequency. Anexception, due to the periodicity of the gratings, is that, formeasurement and reference reflection spetra that are displaced along thefiber by multiples of half the grating length, the corresponding pairsof reflection peaks (e.g., in FIG. 7A, the pair of peaks 720, 722, andthe pair of peaks 728, 730 half a grating period to the left) have thesame frequency distance, and thus result in a single correlation peakacross frequency. The resulting ambiguity in correlation peaks does,however, not cause confusion about which peak is the correct solution(as could create false positives) if the grating length is chosen suchthat any time-delay shifts in excess of half the grating length arenon-physical. For a fiber-sensing application with a one-meter sensinglength, a grating length of at least 2.5 mm limits permitted strains to1250 microstrain.

Beneficially, the presence of at least two correlation peaks acrossfrequency in most time slices of the correlation signal allowsestimating the location of the (higher-amplitude) correlation peakacross both time delay and frequency shift: from cross-correlationscomputed merely for two or more discrete time delays, the estimatedlocation can be found by fitting two curves to the correlation peaksidentified in the cross-correlations for the two or more discrete timedelays and extrapolating to find their intersection. Based on theestimated location, the search space for the correlation peak acrosstime delay and frequency shift can be reduced, saving computational costand speeding up the process of identifying matching locations along thefiber for each measurement spectrum.

With reference to FIGS. 8A and 8B, as another example of gratingconfigurations in accordance with various embodiments, a Braggreflection spectrogram and associated correlation signal, respectively,for an optical fiber including a set of chirped gratings overlappingwith a single-frequency grating are shown. In the depicted example, ascan be seen in FIG. 8A, the Bragg frequency of the single-frequencygrating falls within the range of frequencies spanned by the chirpedgratings. As shown in the example correlation signal of FIG. 8B, thecorrelation signal resulting from correlating, with the reference signalof FIG. 8A, a Bragg reflection spectrum acquired with the same opticalfiber for a given time delay forms a set of parallel pairs of diagonallines (each pair of lines corresponding to one of the chirped gratings)intersecting a pair of horizontal lines (corresponding to thesingle-frequency grating). Thus, the correlation signal exhibitsdistinct correlation peaks with pairs of peaks that repeat every gratinglength. While the two correlation peaks for each chirped grating resultin some ambiguity, this ambiguity can be resolved if the distancebetween these peaks is long enough to render only one of the peaksphysical, that is, within the range of expected time-delay shifts. Ingeneral, the distance between the peaks varies as a function of thedelay associated with the measurement spectrum from which thecorrelation signal is computed, such that some, but not all of the peakscan be disambiguated based on the correlation signal alone. For theremaining pairs of correlation peaks, disambiguation can be achieved byextrapolation from disambiguated peaks in their vicinity, based on theassumption that the correlation peaks shift continuously with timedelay.

Both FIG. 7A and FIG. 8A show grating configurations that use sets ofmultiple consecutive gratings of the same length and chirp rate. Whileit is, in principle, possible to cover the desired frequency range witha single grating (or fewer gratings) with smaller chirp rates, higherchirp rates generally provide for better accuracy in determining thecorrelation peak and, thus, the location of the measured strain.Accordingly, it may be beneficial to set the grating length to a smallvalue that, however, still suffices to exceed the length associated withmaximum expected time-delay shift.

The chirped-grating configurations described herein deliberatelyintroduce controlled broadband features into the fiber, eliminating theneed to rely on imperfections in uniform (i.e., single-frequency)gratings for establishing corresponding points in time delay betweenmeasurement and reference signals. Beneficially, compared with therandom broadband features resulting from imperfections, whichconcentrate all power of the reflection at one frequency, the controlledbroadband features resulting from overlapping chirped gratings generallyprovide better spatial resolution and are less demanding onanalog-to-digital signal conversion of the measured signals. In certaincases, however, the broadband features introduced by overlapping chirpedgratings are less useful than the broadband features inherent in uniformgratings. For example, in the context of a bend measurement (bend beingcomputed from strain in two fiber cores) in the presence of Dopplersignal distortion resulting from a shape change of the fiber during asingle laser scan, uniform gratings provide a more robust bendmeasurement because of differences in the effect of Doppler signaldistortion on the underlying phase tracking algorithm.

To illustrate this problem, refer to FIG. 9 , which shows the amplitude,as a function of time, of a reflection signal obtained with a“herringbone” grating configuration as shown in FIG. 7A. As can be seen,the amplitude includes numerous zeros. With zeros in the signalamplitude, getting good phase measurements will require the referenceand measurement signals to be lined up accurately, and the phasemodulation during a laser scan, resulting from a shape change undergoneby the fiber during the scan, to be approximately linear in time. Thisis not always a good assumption. The fiber may, for example, vibrate,causing sinusoidal time-delay shifts, or may undergo some other stronglynon-linear shape change. In situations where the condition of linearphase modulation is not satisfied, overlapped chirped gratings mayresult in lower accuracy than uniform gratings.

Robustness in bend measurements becomes very important if themeasurement is used in feedback control loops, as are employed tocontrol, e.g., robot joints and the tips of steerable catheters.Especially with high-speed control loops (e.g., operating at about 600Hz or above) generating high forces, an incorrect bend measurement canhave drastic consequences, such as uncontrolled motion. Robust bendmeasurements at joints are also important because the fiber may besubjected to tighter bends and more rapid bend changes in the joints. Inthese cases, some level of uncertainty in the position of the measuredstrain along the fiber (that is, loss of registration in the fibersection at, e.g., the joint or catheter tip) is acceptable if it servesto render the measurement of the bend angle more robust. Accordingly, itcan be beneficial to place single-frequency gratings in the fiber atjoints, steerable cathether tips, and the like.

FIGS. 10A and 10B show example Bragg reflection spectrograms taken withrespective optical fibers including sets of overlapping counter-chirpedfiber gratings consecutive with a single-frequency grating, inaccordance with various embodiments. In FIG. 10A, the single-frequencygrating is located in a mid portion of the optical fiber, between twofiber sections including overlapping sets of chirped gratings. Thesingle-frequency-grating section may be placed, e.g., through a joint. Atypical joint may be between 3 cm and 10 cm in length, allowing theentire length of the single-frequency grating to be written with asuitable phase mask in a single step. FIG. 10B illustrates asingle-frequency grating placed at an end portion (e.g., the tip) of theoptical fiber, where, e.g., a steerable catheter tip may be located. Inmost applications, the single-frequency grating sections of fiber can bekept relatively short (e.g., at less than 10 cm) compared with the totallength of the fiber. Delays accumulate along the length of the fiber,and small lengths of fiber with single-frequency gratings willaccumulate a correspondingly small amount of delay error.

FIG. 11 is a flow chart illustrating a method 1100 of measuring strainalong an optical fiber with overlapping sets of gratings, in accordancewith various embodiments. The fiber includes at least two overlappingsets of gratings inscribed in a fiber core, wherein a first one of thesets of gratings includes one or more chirped gratings and a second oneof the set of gratings includes one or more gratings that are either notchirped at all or are chirped differently than the grating(s) of thefirst set. The method 1100 includes interrogating the optical fiber in areference state of the fiber to obtain a reference signal includingfirst time-delay-dependent reflection spectra (“reflection spectra”)resulting from combined reflections off the two (or more) sets ofgratings (act 1102); each time delay of these first time-delay-dependentreflection spectra corresponds to an associated physical position alongthe fiber. The method 1100 further includes interrogating the opticalfiber in a strained state of the fiber to obtain a measurement signalincluding second time-delay-dependent reflection spectra (“measurementspectra”) likewise resulting from combined reflections off the two (ormore) sets of gratings (act 1104).

The reference reflection spectra are cross-correlated in frequency withthe measurement reflection spectra to determine correlation maximaacross time delay and frequency, each correlation maximum correspondingto a pair of one of the reference reflection spectra and one of themeasurement reflection spectra and to a frequency shift therebetween(act 1106). For example, each of the measurement reflection spectra maybe cross-correlated with a respective plurality of reference spectra(covering a range of time delays including the time delay associatedwith the respective measurement reflection spectrum) to determine acorrelation maximum across the time delays associated with the pluralityof reference reflection spectra and across frequency. Alternatively, foreach of the plurality of positions along the fiber, the associatedreference reflection spectrum may be correlated with a plurality of themeasurement reflection spectra to determine a correlation maximum acrosstime delays of the measurement reflection spectra and across frequencyfor that position along the fiber.

In some embodiments, a full search over the entire possible range oftime-delay shifts (between reference and measurement spectra) andfrequency shifts is performed, at a specified resolution (correspondingto increments in time delay and frequency shift), to identify thecorrelation maximum for each correlation signal (c(t′, Δf|t) or c(t,Δf|t′)). In other embodiments, correlation maxima across frequency,including a correlation maximum associated with the first set ofgratings and a correlation maximum associated with the second set ofgratings, are determined for two or more discrete time-delay shifts (act1108) to estimate a location of the correlation maximum by extrapolationfrom those correlation maxima (act 1110), and the search for thecorrelation maximum is then performed (in act 1106) near an estimatedlocation of the correlation maximum. From the time delays and associatedfrequency shifts of the correlation maxima determined in act 1106,strain along the optical fiber can be computed (act 1112). In someembodiments, simultaneous strain measurements for multiple cores of asingle fiber are further processed, in accordance with techniqueswell-known in the art, to determine the three-dimensional fiber shape(act 1114).

FIG. 12 is a block diagram of an example strain measurement system 1200in accordance with various embodiments. The system 1200 implementsswept-wavelength interferometry (such as OFDR), and includes a tunablelight source 1202 (usually a laser, although other light sources may beused), an interferometric interrogator network 1204, a laser monitornetwork 1206, an optical fiber 1208 serving as a distributed sensor, adata acquisition unit 1210, and a computing system 1212 serving assystem controller and computational processing unit (and thus alsoreferred to as “computational processing unit 1212” herein). Thecomputing system 1212 includes a suitable combination of hardware andsoftware, such as one or more general-purpose hardware processors (e.g.,central processing units (CPUs)) executing software programs and/or oneor more special-purpose hardware processors or circuitry (such as, e.g.,application-specific integrated circuits (ASICs), field-programmablegate arrays (FPGs), or digital signal processors (DSPs)). The computingsystem 1212 may be implemented as a single device, or with multiple(intercommunicating) devices, such as, e.g., separate devices for thesystem controller, which controls the operation of the light source 1202and/or other actively controlled system components, and for thecomputational processing unit, which processes raw data received fromthe data-acquisition unit 1210.

The optical fiber 1208 may be a single-core fiber or, as shown, amulti-core fiber, depending on its use. A single fiber core can be usedfor distributed strain sensing. For shape-sensing applications, amulti-core fiber including, for example, a center core (or waveguide)located about the central axis of the fiber and three or more outercores (waveguides) arranged helically around the center core at a givenradial distance therefrom may be used. Strain measurements taken alongthe length of each core, in conjunction with knowledge of the relativepositions of the cores along the length of the shape-sensing fiber, canbe combined to obtain a strain profile of the fiber (e.g., includingmeasures of bend, twist, and axial strains), from which thethree-dimensional position and orientation of the fiber can bereconstructed. To facilitate strain delay registration in accordanceherewith, each core of the optical fiber 1208 includes two or moreoverlapping sets of gratings differing in chirp. In some embodiments,the gratings extend along the entire length of the fiber 1208 tofacilitate strain measurements at each position along the fiber 1208.While the two or more overlapping sets of gratings may extend over largefiber sections, overlap may be interrupted in one or more short fibersections (e.g., located at fiber bends or at the fiber tip) containingonly a single-frequency grating, e.g., as described with respect toFIGS. 10A and 10B. In various medical applications, a (distal) sectionof the optical fiber may be located inside a catheter. The distal end ofthe catheter, where a medical device (e.g., a surgical tool) may belocated, may be steerable. For robust strain measurements in thatregion, a single-frequency grating may be located near the tip of thatcatheter.

During an OFDR measurement, the light source 1202 is swept through arange of wavelengths (or frequencies). Light emitted by the light source1202 is split with the use of optical couplers and routed to the lasermonitor network 1206 and the interferometric interrogator network 1204.The laser monitor network 1206 may contain a Hydrogen Cyanide (HCN) gascell 1214 that provides an absolute wavelength reference throughout themeasurement scan, and an interferometer 1216 used to measurefluctuations in tuning rate as the light source 1202 is scanned throughthe wavelength range. The interferometric interrogator network 1204 mayinclude one or more interferometric interrogators, generally one foreach core of the optical fiber 1208. In the depicted example system1200, a four-channel system having four interferometric interrogators isused to interrogate a multi-core fiber 1208 suitable for shape sensing.Light enters the core(s) of the optical fiber 1208 through themeasurement arm(s) 1218 of the interferometric interrogator(s). Lightbackscattered in the optical sensing fiber 1208, coupled back into themeasurement arm(s) 1218, and exiting the measurement arm(s) 1218 is theninterfered with light that has traveled along and is exiting thereference arm(s) 1220 of the interferometric interrogator(s). One ormore optical polarization beam splitters separate the resultinginterference pattern(s) each into two orthogonal polarizationcomponents, which are measured by two detectors (e.g., photodiodes) ofthe acquisition unit 1210 (the two detectors collectively constituting apolarization-diverse optical detector). Each of the interferometricinterrogators is being coupled to the tunable light source 1202 viaoptical couplers, and as the tunable light source 1202 is swept across afrequency range, the interference patterns from all channels aresimultaneously measured by respective polarization-diverse opticaldetectors, and processed independently. The optical detectors measuringthe interference pattern(s) generated in the interferometricinterrogator network 1204, and additional detectors in the dataacquisition unit 1210 for measuring light signals from the gas cell 1214and interferometer 1216 of the laser monitor network 1206, convert thereceived light into electrical signals.

The computational processing unit 1212 can process the electricalsignals resulting from the measured interference pattern for the twopolarization states to determine, e.g., the strain in each fiber core asa function position along the fiber. In more detail, in someembodiments, the data acquisition unit 1210 uses the information fromthe laser monitor network 1206 to resample the detected interferencepattern of the optical fiber 1208 to obtain samples at incrementsconstant in optical frequency. Once resampled, the data isFourier-transformed by the computational processing unit 1212 to producea reflection signal in the temporal domain, corresponding to theamplitudes of the reflection signal as a function of time delay alongthe length of the optical fiber 1208. Using the distance that lighttravels in a given increment of time, this delay can be converted to ameasure of length along the sensing fiber 1408. The sampling perioddetermines the spatial resolution and is inversely proportional to thefrequency range that the tunable light source 1202 was swept throughduring the measurement. As the optical fiber 1208 is strained, the localreflections shift in frequency and/or as the optical fiber 1208 changesin physical length. These distortions are highly repeatable. Hence, anOFDR measurement of reflected light for the optical fiber 1208 can beretained in memory to serve as a reference signal of the sensing fiberin an unstrained state. A subsequently measured reflection signal whenthe fiber 1208 is under strain may then be correlated with thisreference signal by the computational processing system 1212, inaccordance with the method described above, to determine the frequencyshift as a function of location along the optical fiber 1208.

FIG. 13 is a block diagram of an example computing system 1500 forcomputing strain along an optical fiber with overlapping gratings basedon correlations between measurement and reference signals (correspondingto acts 1106-1112 in FIG. 11 ), that is, a system implementing thecomputational functionality of the computational processing unit 1212.The system 1300 may be implemented by general-purpose computer hardwareexecuting suitable software, although implementations withspecial-purpose hardware (or combinations of general-purpose andspecial-purpose hardware) are also conceivable. As shown, the system1300 may include one or more processors 1302 (such as single-core ormulti-core CPUs or graphics processing units (GPUs)), (volatile) mainmemory 1304 (e.g., random access memory (RAM)), non-removable and/orremovable permanent data storage 1306 including one or morenon-transitory machine-readable media and associated drives (e.g., harddisks, optical storage devices, etc.), input/output devices 1308 (e.g.,keyboard, mouse, display device, printer, etc.), one or more networkinterfaces 1310, and one or more buses 1312 communicativelyinterconnecting the other system components. Although shown as a singledevice, the system 1300 may, alternatively, be implemented with multipledevices that communicate with each other via one or more wired orwireless networks, connecting to the network(s) via the networkinterfaces 1310.

To implement the computational functionality described above, suitableprocessor-executable software instructions 1314, and the data 1316 theyoperate on (e.g., measured reflection signals, reference spectra,results of computations) may be stored in the data storage 1306 and,during execution of the software, in the main memory 1304. As shown inmore detail within the main memory 1304 (but also applicable to the datastorage 1306), the instructions may be grouped into multiple softwaremodules or components, each providing a distinct part of the overallfunctionality. For example, spectrum generator 1318 may process the rawdata acquired in each measurement to compute a reflection signal as afunction of time delay and frequency; correlator 1320 may compute thecross-correlation between any pair of spectra; peak finder 1322 maydetermine correlations maxima in a correlation signal, across frequencyfor a given time delay, or across both frequency and time delay; peakestimator 1324 may fit lines to correlation peaks across frequencydetermined at multiple discrete time delays, and extrapolate to theintersection of the lines to determine an approximate location of thecorrelation peak across time delay and frequency shift; strain-profilegenerator 1326 may compute strain along the fiber based on thecorrelation peaks; and flow controller 1328 may coordinate the operationof the other components, e.g., to instruct the correlator 1320 whichspectra to correlate, to assemble the resulting one-dimensionalcorrelations into a two-dimensional correlation signal, to determine therange of frequency shifts and time delays over which the search for themaximum is performed by the peak finder 1322, etc. Of course, thedepicted organization into components is only one among many differentpossibilities.

As will be readily appreciated by one of ordinary skill in the art, thesoftware components 1318-1328 (or some subset thereof, or different setof components providing some or all of their functionality) may beembodied on a non-transitory machine-readable medium whether integratedinto a system such as the computing system 1300 or provided aparttherefrom. The term “machine-readable medium” shall be taken to includeany tangible medium that is capable of storing, encoding or carryinginstructions for execution by a machine, or that is capable of storingor encoding data structures used by or associated with suchinstructions. The term “machine-readable medium” shall accordingly betaken to include, but not be limited to, solid-state memories andoptical and magnetic media. Specific examples of machine-readable mediainclude non-volatile memory, including by way of example, semiconductormemory devices (e.g., Erasable Programmable Read-Only Memory (EPROM),Electrically Erasable Programmable Read-Only Memory (EEPROM)) and flashmemory devices; magnetic disks such as internal hard disks and removabledisks; magneto-optical disks; and CD-ROM and DVD-ROM disks. All suchmachine-readable storage media are hardware devices suitable for storingdata and/or instructions for a suitable period of time to enable use bythe machine, and are therefore non-transitory.

While the disclosed subject matter has been described and explainedherein with respect to various example embodiments, these examples areintended as illustrative only and not as limiting. Variousmodifications, additional combinations of features, and furtherapplications of the described embodiments that do not depart from thescope of the subject matter may occur to those of ordinary skill in theart. Accordingly, the scope of the inventive subject matter is to bedetermined by the scope of the following claims and all additionalclaims supported by the present disclosure, and all equivalents of suchclaims.

What is claimed is:
 1. A strain measurement system comprising: anoptical fiber comprising a fiber core including at least two overlappingsets of gratings, the at least two overlapping sets of gratings havingchirp rates that differ in direction or in magnitude or in bothdirection and magnitude; interrogation means for coupling light into thefiber core and measuring a time-domain reflection signal resulting fromreflections of the light off the at least two overlapping sets ofgratings; and computational processing means comprising: conversionmeans for converting the measured time-domain reflection signal into aplurality of measurement reflection spectra associated with differenttime delays; mapping means for mapping each measurement reflectionspectrum of the plurality of measurement reflection spectra to areference reflection spectrum of a plurality of reference reflectionspectra and to an associated frequency shift between the measurementreflection spectrum and the reference reflection spectrum, whereby theassociated frequency shift is associated with a unique locationcorresponding to the reference reflection spectrum; and straindetermination means for determining, based on the associated frequencyshifts, strain in the fiber core along the optical fiber.
 2. The systemof claim 1, wherein the mapping means are configured to map themeasurement reflection spectrum by, for each measurement reflectionspectrum of the plurality of measurement reflection spectra: assemblingcorrelations of the measurement reflection spectrum with the pluralityof reference reflection spectra into a correlation signal as a functionof time-delay shift and frequency; and determining a correlation peak inthe correlation signal.
 3. The system of claim 1, wherein the mappingmeans are configured to map the measurement reflection spectrum by, foreach reference reflection spectrum of the plurality of referencereflection spectra: assembling correlations of the plurality ofmeasurement reflection spectra with the reference reflection spectruminto a correlation signal as a function of time-delay shift andfrequency; and determining a correlation peak in the correlation signal.4. The system of claim 1, wherein the computational processing meansfurther comprise: correlation means for correlating each measurementreflection spectrum with the plurality of reference reflection spectraover a range of time-delay shifts between the measurement reflectionspectrum and the plurality of reference reflection spectra, wherein themapping means are configured to map the measurement reflection spectrumbased on the correlating.
 5. The system of claim 4, wherein the mappingmeans are configured to map each measurement reflection spectrum to areference reflection spectrum by: estimating an estimated location of acorrelation peak by extrapolation from pairs of correlation maximaacross frequency at two or more time-delay shifts of the range oftime-delay shifts, each pair of correlation maxima associated with afirst grating of the first set of gratings and a second grating of thesecond set of gratings; and determining the correlation peak across therange of time-delay shifts and across frequency by performing a searchnear the estimated location.
 6. The system of claim 4, wherein, for eachmeasurement reflection spectrum of the plurality of measurementreflection spectra, the range of time-delay shifts is a symmetric rangecovering, at a specified resolution, time-delay shifts up to an expectedmaximum time-delay shift in both directions from zero time-delay shiftbetween measurement reflection spectrum and reference reflectionspectrum.
 7. The system of claim 1, wherein the conversion means areconfigured to convert the measured time-domain reflection signal into aplurality of measurement reflection spectra associated with differenttime delays by: processing the measured time-domain reflection signal byshort-time Fourier transform.
 8. The system of claim 1, wherein: theoptical fiber comprises one or more additional fiber cores, eachadditional fiber core including at least two additional overlapping setsof additional gratings having chirp rates that differ in direction or inmagnitude or in both direction and magnitude; and the straindetermination means are further configured to determine strain in theadditional fiber cores along the optical fiber.
 9. The system of claim8, wherein: the fiber core and the one or more additional fiber corestogether comprise a central core and at least three helical outer cores;and the computational processing means further comprise shapedetermination means for determining bend, twist, and axial strain alongthe optical fiber from the determined strain for the fiber core and theone or more additional fiber cores along the optical fiber.
 10. Thesystem of claim 9, wherein the shape determination mans are furtherconfigured to determine a three-dimensional position and orientation ofthe optical fiber from the determined bend, twist, and axial strain. 11.A strain measurement system comprising: an optical fiber comprising afiber core having overlapping first and second sets of gratings, whereinthe first set of gratings comprises one or more chirped gratingsextending over a section of the fiber, and wherein the second set ofgratings comprises one or more gratings extending over the section ofthe fiber, the one or more gratings of the second set of gratings notbeing chirped like the one or more chirped gratings of the first set ofgratings; interrogation means for coupling light into the fiber core andmeasuring reflection signals resulting from combined reflections of thelight off the first and second sets of gratings; and computationalprocessing means comprising: conversion means for converting themeasured reflection signals to time-delay-dependent reflection spectra,correlation means for correlating the time-delay-dependent reflectionspectra with time-delay-dependent reference reflection spectra todetermine correlation maxima across time delay and frequency, eachcorrelation maximum corresponding to a pair of a first spectrum of thetime-delay dependent reflection spectra and a second spectrum of thetime-delay-dependent reference reflection spectra, and to a frequencyshift between the first spectrum and the second spectrum of the pair,and, strain determination means for computing, for each correlationmaximum of the correlation maxima, a strain at a position along thefiber associated with the second spectrum corresponding to thecorrelation maximum from an associated frequency shift.
 12. The strainmeasurement system of claim 11, wherein the optical fiber comprises oneor more additional fiber cores, each additional fiber core comprisingtwo overlapping sets of gratings, wherein a first set of the twooverlapping sets of gratings comprises one or more chirped gratingsextending over the section of the fiber, wherein a second set one of thetwo overlapping sets of gratings comprises one or more gratingsextending over the section of the fiber, and wherein the one or moregratings of the second set of the two overlapping sets of gratings arenot chirped like the one or more chirped gratings of the first set ofthe two overlapping sets of gratings.
 13. The strain measurement systemof claim 12, wherein the fiber core and the one or more additional fibercores comprise a central fiber core and at least three peripheral fibercores helically wound around the central fiber core.
 14. The strainmeasurement system of claim 13, wherein the computational processingmeans further comprise: shape determination means for computing, foreach position of a plurality of positions along the fiber and from theassociated frequency shifts determined for the fiber core and the one ormore additional fiber cores, an axial strain, a bend strain, and a twiststrain.
 15. The strain measurement system of claim 11, wherein the oneor more gratings of the second set of gratings are chirped in anopposite direction to the one or more chirped gratings of the first setof gratings.
 16. The strain measurement system of claim 11, furthercomprising a single-frequency grating, wherein the single-frequencygrating and the one or more chirped gratings of the first set ofgratings are consecutive gratings.
 17. The strain measurement system ofclaim 16, further comprising: a catheter, wherein the section of theoptical fiber is located inside the catheter and wherein thesingle-frequency grating is located near a tip of the catheter.
 18. Anoptical fiber sensor comprising: a fiber core comprising: a first set ofgratings, the first set of gratings being chirped, a second set ofgratings overlapping with the first set of gratings in at least a firstsection of the fiber core, wherein the first and second sets of gratingsdiffer in at least one characteristic selected from the group consistingof: being chirped or not chirped, chirp direction, and magnitude. 19.The optical fiber sensor of claim 18, wherein the second set of gratingsare chirped gratings, wherein the first and second sets differ in chirpdirection, and wherein the fiber core further comprises: asingle-frequency grating extending through a second section of the fibercore, the second section being adjacent to the first section.
 20. Theoptical fiber sensor of claim 18, wherein the fiber core is a firstfiber core, and wherein the optical fiber sensor further comprises: asecond fiber core comprising: a third set of gratings, the third set ofgratings being chirped, and a fourth set of gratings overlapping withthe first set of gratings in at least a first section of the secondfiber core, wherein the third and fourth sets of gratings differ in atleast one characteristic selected from the group consisting of: beingchirped or not chirped, chirp direction, and magnitude, and wherein thefirst section of the first fiber core and the first section of thesecond fiber core both correspond to a same portion of the optical fibersensor.